Five variables — Δx, v₀, v, a, t — and four equations, each one leaving exactly one variable out.
| Equation | Leaves out |
|---|---|
| v = v₀ + at | Δx |
| Δx = v₀t + ½at² | v |
| v² = v₀² + 2aΔx | t |
| Δx = ½(v₀ + v)t | a |
Find the variable a problem never mentions, and you've found which equation to reach for.
🧭 Plot Summary
Lesson 1-2-1 gave you three moves for reading a graph: height, slope, and area. Today those three moves turn into four algebraic equations — the kinematic equations — that work whenever acceleration is constant. You won't need to derive them from a graph every time you solve a problem, but you'll always be able to, because that's exactly where they come from.
The real skill this lesson builds isn't memorizing four formulas — it's the missing-variable strategy: look at what a problem gives you and what it's asking for, notice which of the five variables never shows up, and let that tell you which equation to use. No guessing, no "which type of problem is this."
What you will do in this lesson
- Meet the five kinematic variables — Δx, v₀, v, a, t — and the four equations built from them.
- Connect each equation back to a slope or area relationship from Lesson 1-2-1's graphs.
- Learn the missing-variable strategy: identify what a problem doesn't give you, and let that choose your equation.
- Practice single-step problems, then chain them into multi-step problems.
- Confirm, every time, that constant acceleration is a safe assumption before reaching for any of these four equations.
Why it matters
Project 1-2-3: Reconstruct the Ride hands you real velocity data and asks how far something went, how hard it accelerated, and where it ends up next — three questions these four equations answer directly, if you pick the right one each time.
✅ Self-Check Before You Roll On
Check off each item as you get there. These are not grades — they are your own signal.